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Carrier dynamics plays an important role in the transient behavior and frequency response of semiconductor devices. Here, we use two tutorial models of PIN rectifiers in the Semiconductor Module, an add-on to the COMSOL Multiphysics® software, to demonstrate the simulation of dynamical effects.

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Traps are omnipresent in practical semiconductor devices. When modeling these devices, the Trap-Assisted Surface Recombination boundary condition adds the effects of charging and carrier capturing/releasing by surface or interface traps. Here, we examine a tutorial model of a metal-oxide-silicon capacitor (MOSCAP) to demonstrate how to use the feature in the Semiconductor Module, an add-on product to the COMSOL Multiphysics® software.

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The Schrödinger-Poisson Equation multiphysics interface simulates systems with quantum-confined charge carriers, such as quantum wells, wires, and dots. Here, we examine a benchmark model of a GaAs nanowire to demonstrate how to use this feature in the Semiconductor Module, an add-on product to the COMSOL Multiphysics® software.

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The shortest route between two points isn’t necessarily a straight line. If by shortest route, we mean the route that takes the least amount of time to travel from point A to point B, and the two points are at different elevations, then due to gravity, the shortest route is the brachistochrone curve. In this blog post, we demonstrate how to use built-in mathematical expressions and the Optimization Module in COMSOL Multiphysics to solve for the brachistochrone curve.

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Previously in our weak form series, we discretized the weak form equation to obtain a matrix equation to solve for the unknown coefficients in our simple example problem. Following the same procedure as in this previous blog post, we will implement the equation in the COMSOL Multiphysics® software with additional steps included to examine the matrices. We will find it more convenient to use a COMSOL® software application to display all relevant matrices at once, arranged logically on one screen.

Categories

This post continues our blog series on the weak formulation. In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments. Today, we will start to take a behind-the-scenes look at how the equations are discretized and solved numerically.

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The effect of quantum tunneling can be important if the thickness of the energy barrier for the charge carrier is comparable to or smaller than the evanescent decay length. In order to account for this effect, we can use the WKB Tunneling Model feature, available in the Semiconductor Module as of version 5.4 of the COMSOL® software, for the heterojunction and Schottky contact boundary conditions. Here, we demonstrate their usage using a benchmark model.

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You can use the new Schrödinger Equation interface for modeling with the Semiconductor Module in the latest release of the COMSOL® software. Let’s look at a simple example app that uses this interface to estimate the electron and hole ground state energy levels for a superlattice structure. By building apps like this one, device engineers are able to calculate the band gap for a given periodic structure and adjust the design parameters until a desired band gap value is achieved.

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Today we continue our discussion on the weak formulation by looking at how to implement a point source with the weak form. A point source is a useful tool for idealizing the situation where a source is concentrated in a very small region of the modeling domain. We will find that it is very convenient to set up such a point source using the weak form.

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Over half a century ago, Mark Kac gave an interesting lecture on a question that he had heard from Professor Bochner ten years earlier: “Can one hear the shape of a drum?” He focused on the (then undetermined) uniqueness of the set of eigenvalues given the shape of a vibrating membrane. The eigenvalue problem has since been solved and here we explore the “hearing” part of the question by considering some interesting physical effects.

Categories

This blog post is part of a series aimed at introducing the weak form with minimal prerequisites. In the first blog post, we learned about the basic concepts of the weak formulation. All equations were left in the analytical form. Today, we will implement and solve the equations numerically using the COMSOL Multiphysics simulation software. You are encouraged to follow the steps with a working copy of the COMSOL software.

Categories

Traps are omnipresent in practical semiconductor devices. When modeling these devices, the Trap-Assisted Surface Recombination boundary condition adds the effects of charging and carrier capturing/releasing by surface or interface traps. Here, we examine a tutorial model of a metal-oxide-silicon capacitor (MOSCAP) to demonstrate how to use the feature in the Semiconductor Module, an add-on product to the COMSOL Multiphysics® software.

Categories

The effect of quantum tunneling can be important if the thickness of the energy barrier for the charge carrier is comparable to or smaller than the evanescent decay length. In order to account for this effect, we can use the WKB Tunneling Model feature, available in the Semiconductor Module as of version 5.4 of the COMSOL® software, for the heterojunction and Schottky contact boundary conditions. Here, we demonstrate their usage using a benchmark model.

Categories

The Schrödinger-Poisson Equation multiphysics interface simulates systems with quantum-confined charge carriers, such as quantum wells, wires, and dots. Here, we examine a benchmark model of a GaAs nanowire to demonstrate how to use this feature in the Semiconductor Module, an add-on product to the COMSOL Multiphysics® software.

Categories

You can use the new Schrödinger Equation interface for modeling with the Semiconductor Module in the latest release of the COMSOL® software. Let’s look at a simple example app that uses this interface to estimate the electron and hole ground state energy levels for a superlattice structure. By building apps like this one, device engineers are able to calculate the band gap for a given periodic structure and adjust the design parameters until a desired band gap value is achieved.

Categories

The shortest route between two points isn’t necessarily a straight line. If by shortest route, we mean the route that takes the least amount of time to travel from point A to point B, and the two points are at different elevations, then due to gravity, the shortest route is the brachistochrone curve. In this blog post, we demonstrate how to use built-in mathematical expressions and the Optimization Module in COMSOL Multiphysics to solve for the brachistochrone curve.

Categories

Today we continue our discussion on the weak formulation by looking at how to implement a point source with the weak form. A point source is a useful tool for idealizing the situation where a source is concentrated in a very small region of the modeling domain. We will find that it is very convenient to set up such a point source using the weak form.

Categories

Previously in our weak form series, we discretized the weak form equation to obtain a matrix equation to solve for the unknown coefficients in our simple example problem. Following the same procedure as in this previous blog post, we will implement the equation in the COMSOL Multiphysics® software with additional steps included to examine the matrices. We will find it more convenient to use a COMSOL® software application to display all relevant matrices at once, arranged logically on one screen.

Categories

Over half a century ago, Mark Kac gave an interesting lecture on a question that he had heard from Professor Bochner ten years earlier: “Can one hear the shape of a drum?” He focused on the (then undetermined) uniqueness of the set of eigenvalues given the shape of a vibrating membrane. The eigenvalue problem has since been solved and here we explore the “hearing” part of the question by considering some interesting physical effects.

Categories

This post continues our blog series on the weak formulation. In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments. Today, we will start to take a behind-the-scenes look at how the equations are discretized and solved numerically.

Categories

This blog post is part of a series aimed at introducing the weak form with minimal prerequisites. In the first blog post, we learned about the basic concepts of the weak formulation. All equations were left in the analytical form. Today, we will implement and solve the equations numerically using the COMSOL Multiphysics simulation software. You are encouraged to follow the steps with a working copy of the COMSOL software.